This calculator analyzes four variables in a balanced three-phase AC circuit: total real power in kilowatts, line-to-line RMS voltage, line RMS current, and power factor. Enter any three and it returns the fourth, so you can check measured load, estimate current draw, or identify the power factor implied by a set of readings.
The formula
kW = √3 · E · I · PF / 1000. The √3 factor combines the three balanced phase contributions when E is the line-to-line RMS voltage and I is the line RMS current. Multiplying by power factor gives total real power in watts; dividing by 1000 gives kilowatts. Enter power factor as a decimal between 0 and 1 — for example, 0.85 rather than 85.
Use line quantities
Enter the voltage measured between any two supply lines, not line-to-neutral voltage, and enter the current in one line. The compact √3 formula already accounts for the relationship between line and phase quantities in a balanced system, whether the load is connected in wye or delta. Mixing phase voltage with this formula produces the wrong result.
Solve in any direction
- Kilowatts — total real electrical power from known line voltage, line current, and power factor.
- Current — the balanced line amperage required for a known three-phase load.
- Voltage — the line-to-line RMS supply voltage implied by the other readings.
- Power factor — real power divided by apparent power; a result above 1.0 identifies inconsistent inputs.
Kilowatts here mean electrical input power
This calculator returns real electrical power delivered to the load and therefore has no efficiency term. To estimate a motor’s mechanical shaft output, multiply by motor efficiency or use the three-phase horsepower calculator. For a single-phase supply, use the single-phase kilowatt calculator, which does not include the √3 factor.
Balanced three-phase assumption
The compact formula assumes a balanced three-phase supply and load, with substantially equal phase currents and one representative power factor. For materially unbalanced circuits, calculate each phase separately from its phase voltage, current, and power factor, then add the three real-power results.
Worked example
A balanced three-phase load drawing 10 A from a 460 V line-to-line supply at 0.85 power factor has apparent power √3 × 460 × 10 ≈ 7967 VA. Its real power is 7967 × 0.85 ≈ 6772 W, or 6.772 kW.